scholarly journals Additive functionals and excursions of Kuznetsov processes

2005 ◽  
Vol 2005 (13) ◽  
pp. 2031-2040
Author(s):  
Hacène Boutabia
Keyword(s):  
Additive Functional ◽  
Standard Process ◽  
Additive Functionals ◽  
Isolated Points ◽  
Classical Duality

LetBbe a continuous additive functional for a standard process(Xt)t∈ℝ+and let(Yt)t∈ℝbe a stationary Kuznetsov process with the same semigroup of transition. In this paper, we give the excursion laws of(Xt)t∈ℝ+conditioned on the strict past and future without duality hypothesis. We study excursions of a general regenerative system and of a regenerative system consisting of the closure of the set of times the regular points ofBare visited. In both cases, those conditioned excursion laws depend only on two pointsXg−andXd, where]g,d[is an excursion interval of the regenerative setM. We use the(FDt)-predictable exit system to bring together the isolated points ofMand its perfect part and replace the classical optional exit system. This has been a subject in literature before (e.g., Kaspi (1988)) under the classical duality hypothesis. We define an “additive functional” for(Yt)t∈ℝwithB, we generalize the laws cited before to(Yt)t∈ℝ, and we express laws of pairs of excursions.

Disjointly Additive Operators and Modular Spaces

1990 ◽  
Vol 42 (3) ◽  
pp. 508-519
Author(s):  
Iwo Labuda
Keyword(s):  
Additive Functional ◽  
Typical Result ◽  
Additive Functionals ◽  
Modular Spaces ◽  
The Subject ◽  
Image Position

By now the literature concerning the representation of disjointly additive functionals and operators is quite extensive. A few entries on the subject are [6, 7, 8, 11, 20, 21]. In [7, 8, 17] further references can be found, in [7] the “prehistory” of the subject is also discussed.To quote a typical result, we may take a 1967 theorem of Drewnowski and Orlicz ([6] Th. 3.2, [17] 12.4) which asserts that, under proper assumptions, an abstract modular (= disjointly countably additive functional) p on a “substantial“ subspace D of L° can be realized by the formula .

scholarly journals Limit theorems for additive functionals of continuous time random walks

2020 ◽  
pp. 1-22
Author(s):  
Yuri Kondratiev ◽  
Yuliya Mishura ◽  
Georgiy Shevchenko
Keyword(s):  
Continuous Time ◽  
Limit Theorems ◽  
Domain Of Attraction ◽  
Weak Limit ◽  
Additive Functional ◽  
Stable Law ◽  
Additive Functionals ◽  
Lévy Motion ◽  
Continuous Time Random Walks ◽  
Poisson Shot Noise

Abstract For a continuous-time random walk X = {X t , t ⩾ 0} (in general non-Markov), we study the asymptotic behaviour, as t → ∞, of the normalized additive functional $c_t\int _0^{t} f(X_s)\,{\rm d}s$ , t⩾ 0. Similarly to the Markov situation, assuming that the distribution of jumps of X belongs to the domain of attraction to α-stable law with α > 1, we establish the convergence to the local time at zero of an α-stable Lévy motion. We further study a situation where X is delayed by a random environment given by the Poisson shot-noise potential: $\Lambda (x,\gamma )= {\rm e}^{-\sum _{y\in \gamma } \phi (x-y)},$ where $\phi \colon \mathbb R\to [0,\infty )$ is a bounded function decaying sufficiently fast, and γ is a homogeneous Poisson point process, independent of X. We find that in this case the weak limit has both ‘quenched’ component depending on Λ, and a component, where Λ is ‘averaged’.

scholarly journals Stochastic calculus over symmetric Markov processes with time reversal

2015 ◽  
Vol 220 ◽  
pp. 91-148
Author(s):  
K. Kuwae
Keyword(s):  
Markov Processes ◽  
Time Reversal ◽  
Harmonic Functions ◽  
Stochastic Calculus ◽  
Additive Functional ◽  
Zero Energy ◽  
Additive Functionals ◽  
Stochastic Characterization ◽  
Symmetric Markov Processes

AbstractWe develop stochastic calculus for symmetric Markov processes in terms of time reversal operators. For this, we introduce the notion of the progressively additive functional in the strong sense with time-reversible defining sets. Most additive functionals can be regarded as such functionals. We obtain a refined formula between stochastic integrals by martingale additive functionals and those by Nakao's divergence-like continuous additive functionals of zero energy. As an application, we give a stochastic characterization of harmonic functions on a domain with respect to the infinitesimal generator of semigroup on L2-space obtained by lower-order perturbations.

On entrance—exit distributions of Markov processes

1978 ◽  
Vol 15 (01) ◽  
pp. 78-86
Author(s):  
Cristina Gzyl ◽  
Henryk Gzyl
Keyword(s):  
Markov Processes ◽  
Additive Functional ◽  
Stochastic Integrals ◽  
Standard Process ◽  
Integration By Parts ◽  
Infinitesimal Generators ◽  
The Right ◽  
Continuous Inverse ◽  
Exit Distributions

We use a result on integration by parts for stochastic integrals together with a technique developed by Getoor in [6], to express entrance—exit distributions for a standard process X, and a set Φ which is the support of a continuous additive functional C, in terms of the infinitesimal generators of semigroups associated with the time-changed process (X τ t ), where (τ t ) is the right-continuous inverse of C.

Additive Functionals on Lorentz Spaces

1984 ◽  
Vol 27 (1) ◽  
pp. 31-37
Author(s):  
Pratibha G. Ghatage
Keyword(s):  
Sufficient Conditions ◽  
Concave Function ◽  
Additive Functional ◽  
Real Numbers ◽  
Positive Real ◽  
Additive Functionals ◽  
Atomic Measure ◽  
Necessary And Sufficient ◽  
Special Case ◽  
Lorentz Norm

AbstractIf (X, β, μ) is a σ-finite, non-atomic measure space, and ϕ is an increasing non-negative concave function defined on the positive real numbers, we give a set of necessary and sufficient conditions for an additive functional T on the Lorentz space Nϕ to have an integral representation with a Caratheodory kernel. In the special case when T is statistical we classify the functional properties (enjoyed by the kernels) in terms of the Lorentz norm on the space.

scholarly journals On the Measurability of Additive Functionals

2007 ◽  
Vol 14 (1) ◽  
pp. 135-143
Author(s):  
Alexander Kharazishvili
Keyword(s):  
Hilbert Space ◽  
Borel Measure ◽  
Separable Hilbert Space ◽  
Additive Functional ◽  
Special Consideration ◽  
Infinite Dimensional ◽  
Additive Functionals ◽  
Borel Measures

Abstract For an infinite-dimensional separable Hilbert space 𝐻, the problem of measurability of additive functionals 𝑓 : 𝐻 → 𝐑 with respect to various extensions of σ-finite diffused Borel measures on 𝐻 is discussed. It is shown that there exists an everywhere discontinuous additive functional 𝑓 on 𝐻 such that, for any σ-finite diffused Borel measure μ on 𝐻, this 𝑓 can be made measurable with respect to an appropriate extension of μ. Special consideration is given to the case where μ is invariant or quasiinvariant under a subgroup of 𝐻.

On entrance—exit distributions of Markov processes

1978 ◽  
Vol 15 (1) ◽  
pp. 78-86
Author(s):  
Cristina Gzyl ◽  
Henryk Gzyl
Keyword(s):  
Markov Processes ◽  
Additive Functional ◽  
Stochastic Integrals ◽  
Standard Process ◽  
Integration By Parts ◽  
Infinitesimal Generators ◽  
The Right ◽  
Continuous Inverse ◽  
Exit Distributions

We use a result on integration by parts for stochastic integrals together with a technique developed by Getoor in [6], to express entrance—exit distributions for a standard process X, and a set Φ which is the support of a continuous additive functional C, in terms of the infinitesimal generators of semigroups associated with the time-changed process (Xτt), where (τt) is the right-continuous inverse of C.

scholarly journals Stochastic calculus over symmetric Markov processes with time reversal

2015 ◽  
Vol 220 ◽  
pp. 91-148 ◽  
Author(s):  
K. Kuwae
Keyword(s):  
Markov Processes ◽  
Time Reversal ◽  
Harmonic Functions ◽  
Stochastic Calculus ◽  
Additive Functional ◽  
Zero Energy ◽  
Additive Functionals ◽  
Stochastic Characterization ◽  
Symmetric Markov Processes

AbstractWe develop stochastic calculus for symmetric Markov processes in terms of time reversal operators. For this, we introduce the notion of the progressively additive functional in the strong sense with time-reversible defining sets. Most additive functionals can be regarded as such functionals. We obtain a refined formula between stochastic integrals by martingale additive functionals and those by Nakao's divergence-like continuous additive functionals of zero energy. As an application, we give a stochastic characterization of harmonic functions on a domain with respect to the infinitesimal generator of semigroup on L2-space obtained by lower-order perturbations.

Analisis Kesenjangan Pelaksanaan Standar Proses pada Pembelajaran Produktif di SMK

2017 ◽  
Vol 2 (1) ◽  
Author(s):  
Atika Atika ◽  
I Made Sudana ◽  
Basyirun Basyirun
Keyword(s):  
Learning Process ◽  
Lesson Plan ◽  
Lesson Plans ◽  
Ministry Of Education ◽  
Standard Process ◽  
Basic Principles ◽  
Discrepancy Rate ◽  
Quantitative Descriptive ◽  
Concrete Solution ◽  
Evaluation Of Learning

Tujuan penelitian, diantaranya menguraikan bagaimana pelaksanaan standar proses, menganalisis seberapa tingkat kesenjangannya dan merancang bagaimana solusi permasalahan terkait kesenjangan pelaksanan standar proses. Penelitian ini menggunakan penelitian deskriptif dengan pendekatan kuantitatif. Aspek dalam penelitian ini adalah (a) perencanaan pembelajaran; (b) pelaksanaan pembelajaran; (c) penilaian hasil belajar; (d) pengawasan oleh kepala sekolah. Teknik pengumpulaan data, yang digunakan adalah metode observasi, wawancara dan dokumentasi. Hasil Penelitian menunjukkan bahwa dalam hal perencanaan pembelajaran diperoleh kriteria tidak senjang, artinya pada kegiatan perencanaan tidak banyak guru yang mengabaikan standar yang ditetapkan oleh Permendikbud No. 65 tahun 2013. Hasil analisis pelaksanaan pembelajaran diperoleh kriteria cukup senjang, artinya standar proses yang ditetapkan belum sepenuhnya dilaksanakan. Hasil analisis menunjukkan bahwa pada kegiatan penilaian masih diperoleh hasil cukup senjang, artinya masih terdapat ketentuan yang belum diterapkan. Hasil analisis pada komponen pengawasan memberikan kesimpulan jika masih terdapat kepala sekolah yang tidak menjalankan fungsinya sebagai pengawas internal.Therefore, the aims of study are to investigate the implementation of the standard process, analyze the discrepancy rate and design the solution toward the issue of discrepancy. This research uses the quantitative descriptive approach. There are several aspects investigated; (a) lesson plan, (b) learning process, (c) evaluation of learning result, and (d) headmasters control. To collect the data, the methods of observation, interview, and documentation are used. The result is explained in form of criteria. It is no discrepancy for lesson plans, means that most of the lesson plans are in accord with the Basic Principles issued by Ministry of Education and Culture Number 65 in 2013. The learning process has a quite discrepancy rate, means the standard process is incompletely applied; so does the evaluation which ignores several principles to apply. It is also noted that some headmasters ignore their function as an internal supervisor. To sum up, the discrepancy issue needs further concrete solution.

Solutions and Stability of Generalized Mixed Type QCA-Functional Equations in Random Normed Spaces

2013 ◽  
Vol 59 (2) ◽  
pp. 299-320
Author(s):  
M. Eshaghi Gordji ◽  
Y.J. Cho ◽  
H. Khodaei ◽  
M. Ghanifard
Keyword(s):  
Functional Equation ◽  
General Solution ◽  
Functional Equations ◽  
Mixed Type ◽  
Additive Functional ◽  
Normed Spaces ◽  
Additive Functional Equation ◽  
Probabilistic Normed Spaces ◽  
Random Normed Spaces ◽  
Generalized Stability

Abstract In this paper, we investigate the general solution and the generalized stability for the quartic, cubic and additive functional equation (briefly, QCA-functional equation) for any k∈ℤ-{0,±1} in Menger probabilistic normed spaces.

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